Recursion is a new effective method for computing dense linear algebra. It allows for efficient utilization of memory hierarchies of today′s high-performance computers. The recursive algorithm for Cholesky factorization is studied in this paper. A detailed derivation of the recursive Cholesky algorithm is given. The algorithm is then implemented in FORTRAN90 that supports recursion as a language feature. The efficiency of the recursive algorithm is further improved by a method of matrix element reordering. The resulting algorithms are 15%-25% faster than the currently used block algorithm.
